%0 Journal Article
%T A Parametric Learning and Identification Based Robust Iterative Learning Control for Time Varying Delay Systems
%A Lun Zhai
%A Guohui Tian
%A Yan Li
%J Journal of Control Science and Engineering
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/471921
%X A parametric learning based robust iterative learning control (ILC) scheme is applied to the time varying delay multiple-input and multiple-output (MIMO) linear systems. The convergence conditions are derived by using the and linear matrix inequality (LMI) approaches, and the convergence speed is analyzed as well. A practical identification strategy is applied to optimize the learning laws and to improve the robustness and performance of the control system. Numerical simulations are illustrated to validate the above concepts. 1. Introduction Learning mechanism enables the human beings to master skills, while the experiences gained from practices play important roles in this procedure. It is expected that the learning mechanism can also be introduced to machines, which enables them to achieve satisfactory performance from previous acquired input-output information. The method of ILC was firstly applied to control manipulators at high speed which is proposed by Uchiyama [1]. In 1984, Arimoto [2] published the first English paper of ILC for accurate tracking of robot trajectories. The basic idea of ILC is utilizing the information of the previous iteration to realize perfect tracking without exact knowledge of the system parameters, and a typical ILC scheme is shown as in Figure 1. In the recent three decades, many kinds of learning laws are utilized which can be mainly divided by two categories: the linear learning laws and the nonlinear learning laws. For example, the linear learning laws include but are not limited to the parametric learning law [3, 4], the robust learning law [5], the high-order learning law [6, 7], the PD type learning law [8, 9], and so on [10]. On the other hand, the Newton learning law and the Secant learning law belong to the nonlinear ones [11, 12] which have faster convergence speed comparing to some linear cases. Moreover, the control objectives are mainly focused on the linear continuous and discrete forms [13, 14] and the nonlinear systems with relative degree one [15] or the quasilinear forms [16] and so forth [17¨C27]. Figure 1: The basic idea of ILC. The time delay systems are ubiquitous in real world control problems [28] such as networked control systems, chemical processes, hydraulic, and rolling mill systems. The time delay affects the system performance in a large scale. Serious performance degradation and even instability can be led by time delay [29]. For decades, considerable efforts have been paid to assure the robust performance of time delay systems in both theories and applications [30]. The research of time
%U http://www.hindawi.com/journals/jcse/2014/471921/